Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#72233412 |
| Fitting, Sylow | C2×#516323 ⋊ C3 |
| derived | C22×H(5,𝔽2) ⋊ C2×C3×C4 |
88400 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 88400 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72246282, C2×#72252244, C2×C4×#35346⋊C3 |
| maximal normal subgroup of | C2×#72246282, C2×#72252244, C2×C4×#35346⋊C3 |
Past the SmallGroups library coverage — no SmallGroups id.